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We study toric degenerations of opposite Schubert and Richardson varietiesinside degenerations of Grassmannians and flag varieties. These degenerationsare parametrized by matching fields in the sense of Sturmfels and Zelevinsky.We construct so-called restricted matching field ideals whose generating setsare understood combinatorially through tableaux. We determine when these idealsare toric and coincide with Gr\"obner degenerations of Richardson varietiesusing the well established standard monomial theory for Grassmannians and flagvarieties.

Standard monomial theory and toric degenerations of Richardson varieties inside Grassmannians and flag varieties